pajarita

	THE NAZARI BIRD
	Geometry in the art of M.C. Escher

1. HISPANO-ISLAMIC ART. THE ALHAMBRA
The Dutch artist M.C.Escher began working on regular division of the plane (which form part of his most famous works) after visiting the Alhambra in Granada, Spain. The elaborate decoration, based on the harmonious repetition of geometric motifs, many including inscriptions taken from the Koran, fascinated Escher and he started to analyse how these mosaics had been put together.
	1.- One of the most common mosaics found in the palaces which form the group of buildings designed by the Nazari Court (an acropolis and town) during the XIII^th and XIV^th centuries, is that known as the *Nazari* *bird*. Find out what you can about the history, art and culture of the Nazari court in Spain and the effect that Moorish society had on Spain. 2.- Have a look on the Internet or in an encyclopedia for designs which are based on the Nazari bird motif. 3.- Try and work out which polygon the bird is based on. 4.- Note that the plane is covered by a pattern (darker and lighter coloured birds). However, there is another bigger pattern as well covering the plane which is made up of 6 birds. 5.- Show how regular hexagons can be formed from equal-sized equilateral triangles.
6.- Look at the visual effect produced by the design. The spirit of the most highly-skilled Arabic artists was focused on the idea that no point was more special or more important than another. This effect is obtained by using symmetry and reflection and tessellating the plane both uniformly and harmoniously.

2. CONSTRUCTING THE BIRD

The first rule of construction of Escher's tessellations.

The different shapes which make up some of Escher's tessellations can be obtained by using a triangle or quadrilateral as a starting point. A piece is cut out of one of the sides of the shape (no longer than half the length of the side) and it is then added to the same side by rotating it through 180º about the centre of rotation which is found at the mid-point of this side.

7.- Try to construct the bird shape from an equilateral triangle.

8.- Work out which steps you need to take by using the first rule to construct Escher's tessellations.

Click on the Animate button in order to see how the Nazari bird is constructed from an equilateral triangle.

9.- Use the above rule to create your own designs using a polygon as your starting point (either a triangle or a quadrilateral).

10.- What importance does the way the pieces are formed have when they are put together to form a pattern? Design a shape by altering just one side of the polygon and note the choice you have of where the shapes can go when piecing the tessellation together.

11.- Design a house-shaped piece based on a pentagon and try to tessellate the plane with it. What happens? Can we use the above rule in this case?

3. DYNAMIC GEOMETRY IN TESSELLATIONS

In order to adhere to the norms of beauty, harmony and regularity Arabic craftsmen had little choice but to incorporate not only geometry, but dynamic geometry, based on transformations on the plane, into their art.

12.- Find out which movements are needed to transform the yellow bird into one of the turquoise birds in the pattern.

Each time you increase the option parameter by 1 a bird will be indicated for you to work out the transformation. Each of the values of this parameter relates to a different bird in the tessellation.

Make the solution parameter value equal to the option parameter value to check the solution to each problem.

12.- Design similar exercises yourself and work out the relationship between the different pieces.

13.- Is the reflection of the yellow piece used to form any of the other pieces in this tessellation?

	Enrique Martínez Arcos

	© Spanish Ministry of Education and Science. Year 2001